Theme Essential Question: How can you use formulas and geometry to solve real-world and mathematical problems?
Essential Questions:
How can you identify cross sections of three-dimensional figures?
How can you use angle pairs to solve problems?
Standards:
7.G. 3 Describe the two-dimensional figures that results from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to solve simple equations for an unknown angle in a figure.
Objectives:
The student will identify figures formed by cross sections.
The student will sketch cross sections of three dimensional figures.
The student will identify and construct supplementary, complementary, vertical and adjacent angles.
The student will apply knowledge of supplementary, complementary, vertical and adjacent angles to solve multi-step problems and simple equations for an unknown angle.
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team This week will focus on two different concepts; cross-sections of three dimensional figures and angle pairs. In order to facilitate student product, Teaching the Common Core Math Standards with Hands-on Activities, will be used as the primary resource. The discussion provided below from Ohio Department of Education will be very useful in the development of lesson and activities.
Background: Recommended: For a quick overview of the standard(s) to be addressed in this Unit, see Arizona’s Content Standards Reference Materials at**http://www.azed.gov/educator-certification/**
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2022
Cross-Sections: Slicing three-dimensional figures helps develop three-dimensional visualization skills. Students should have the opportunity to physically create some of the three-dimensional figures, slice them in different ways, and describe in pictures and words what has been found. For example, use clay to form a cube, then pull string through it in different angles and record the shape of the slices found. Challenges can also be given: “See how many different two-dimensional figures can be found by slicing a cube” or “What three-dimensional figure can produce a hexagon slice?” This can be repeated with other three-dimensional figures using a chart to record and sketch the figure, slices and resulting two-dimensional figures.
Angle Pairs: In previous grades, students have studied angles by type according to size: acute, obtuse and right, and their role as an attribute in polygons. Now angles are considered based upon the special relationships that exist among them: supplementary, complementary, vertical and adjacent angles. Provide students the opportunities to explore these relationships first through measuring and finding the patterns among the angles of intersecting lines or within polygons, then utilize the relationships to write and solve equations for multi-step problems.
Assessment: Product Teaching the Common Core Math Standards with Hands-on Activities:
Cross-Sections:
Use Acitivity #2, Slicing Figures, page 120
Allow students to work in groups and assign a different shape to each group.
Recommended shapes rectangular prism, cone, cylinder, sphere, triangular pyramid, rectangular pyramid. (other prisms and pyramids as needed).
Slice shape to find as many cross sections, as noted in the activity instructions, and present their cross sections to the class.
If a student(s) have the aptitude to prepare sketches, allow this student(s) to roam the class producing sketches of the cross sections to be use as classroom displays.
Angle Pairs:
Use Activity, What’s the Angle?, page 124
Conduct the activity and display student work as indicated.
Key Questions
What geometric figures are formed from a cross section of a three dimensional shape?
What are the characteristics of supplementary, complementary, vertical and adjacent angles?
How do you apply supplementary, complementary, vertical and adjacent angles to solve multi-step problems and simple equations for an unknown angle?
Observable Student Behaviors
The student can viualize and describe the two-dimensional figures that results from slicing three-dimensional shapes.
The student can use and apply supplementary, complementary, vertical, and adjacent angles in a multi-step problem to solve simple equations for an unknown angle.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Houghton Mifflin On Core Mathematics Middle School Grade 7
Unit 4-3, Cross Sections, p. 97-98
Unit 4-4, Angle Pairs, p. 99-102
ABC Mastering the Common Core in Mathematics
Solid Figures, Chapter 13.1, p. 159
Cross Sections, Chapter 13.2, p. 160-161
Adjacent angles, Chapter 10.2, p. 118
Vertical angles, Chapter 10.3, p. 119
Complementary and Supplementary Angles, Chapter 10.4, p. 120
Finding angles in figures, Chapter 10.5, p. 121
Chapter 10 Review and Test, p. 122-123
Gizmo Correlation:
7.G.5
Investigating Angles Theorems-Activity A
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure.
Teaching the Common Core Math Standards with Hands-On Activities,
7.G.3 – Activity #1, p.119
7.G.3 – Activity #2, p.120
7.G.5 – Activity, p.124
Highly Recommended None Available at this time
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Mathematics in Children's Literature:Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annontated Lists of Children's Literature including the math concepts and grade levels.
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
Describe, analyze and reason about the properties of rectangular prisms. Contruct rectangular prisms and flat patterns using a variety of materials and tools.
Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
Content: Cross Sections
Angle Pairs
Dates: 2/4 – 2/8
Theme Essential Question:
How can you use formulas and geometry to solve real-world and mathematical problems?
Essential Questions:
Standards:
Objectives:
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team
This week will focus on two different concepts; cross-sections of three dimensional figures and angle pairs. In order to facilitate student product, Teaching the Common Core Math Standards with Hands-on Activities, will be used as the primary resource. The discussion provided below from Ohio Department of Education will be very useful in the development of lesson and activities.
Background:
Recommended: For a quick overview of the standard(s) to be addressed in this Unit, see Arizona’s Content Standards Reference Materials at**http://www.azed.gov/educator-certification/**
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2022
Cross-Sections:
Slicing three-dimensional figures helps develop three-dimensional visualization skills. Students should have the opportunity to physically create some of the three-dimensional figures, slice them in different ways, and describe in pictures and words what has been found. For example, use clay to form a cube, then pull string through it in different angles and record the shape of the slices found. Challenges can also be given: “See how many different two-dimensional figures can be found by slicing a cube” or “What three-dimensional figure can produce a hexagon slice?” This can be repeated with other three-dimensional figures using a chart to record and sketch the figure, slices and resulting two-dimensional figures.
Angle Pairs:
In previous grades, students have studied angles by type according to size: acute, obtuse and right, and their role as an attribute in polygons. Now angles are considered based upon the special relationships that exist among them: supplementary, complementary, vertical and adjacent angles. Provide students the opportunities to explore these relationships first through measuring and finding the patterns among the angles of intersecting lines or within polygons, then utilize the relationships to write and solve equations for multi-step problems.
Assessment:
Product
Teaching the Common Core Math Standards with Hands-on Activities:
- Cross-Sections:
Use Acitivity #2, Slicing Figures, page 120- Angle Pairs:
Use Activity, What’s the Angle?, page 124Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary:
Congruent angles Vertical angles Adjacent angles
Complementary angles Congruent angles Supplementary angles
Suggested Activities:
- Houghton Mifflin On Core Mathematics Middle School Grade 7
- Unit 4-3, Cross Sections, p. 97-98
- Unit 4-4, Angle Pairs, p. 99-102
- ABC Mastering the Common Core in Mathematics
- Solid Figures, Chapter 13.1, p. 159
- Cross Sections, Chapter 13.2, p. 160-161
- Adjacent angles, Chapter 10.2, p. 118
- Vertical angles, Chapter 10.3, p. 119
- Complementary and Supplementary Angles, Chapter 10.4, p. 120
- Finding angles in figures, Chapter 10.5, p. 121
- Chapter 10 Review and Test, p. 122-123
- Gizmo Correlation:
- 7.G.5
- Investigating Angles Theorems-Activity A
- Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure.
- Teaching the Common Core Math Standards with Hands-On Activities,
- 7.G.3 – Activity #1, p.119
- 7.G.3 – Activity #2, p.120
- 7.G.5 – Activity, p.124
- Highly Recommended None Available at this time
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.- Glencoe, Pre-Algebra, Chapter 11.4, p. 581
- Glencoe, Geometry, p. 639, 640, 641, 648
- Create a puzzle with unit vocabulary words.
http://www.discoveryeducation.com/free-puzzlemaker/?CFID=1276695&CFTOKEN=75709576Diverse Learners
Homework: (Teachers Discretion)
Terminology for Teachers:
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking| Reinforcing/Recognition| Homework/Practice |
Non-Linguistic representation| Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources:
Professional Texts:
Literary Texts
- Geometry and Literature Titles:
http://sci.tamucc.edu/~eyoung/geometry_literature.html- Measurement and children'e Literature/Ratios
http://sci.tamucc.edu/~eyoung/measure_literature.html- Mathematics in Children's Literature:Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annontated Lists of Children's Literature including the math concepts and grade levels.
Click on the following link, http://libguides.nl.edu/mathinchildrenslit, then look under Math and Literature Bibliographies.- Middle & High School: Literature in Mathematics
Many books include websites with lesson ideas.http://sci.tamucc.edu/~eyoung/middle_school_literature.html
- Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine)
http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html- Miscellaneous Math and Children's Literature
http://sci.tamucc.edu/~eyoung/literature.htmlInformational Texts
Art, Music, and Media
Manipulatives:
Games
Videos
SMART Board Lessons, Promethean Lessons
- 7. G. 3 Rectangular Prisms
Describe, analyze and reason about the properties of rectangular prisms. Contruct rectangular prisms and flat patterns using a variety of materials and tools.Other Activities, etc.
- Puzzle Maker
- http://www.discoveryeducation.com/free-puzzlemaker/?CFID=1276695&CFTOKEN=75709576
- Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
http://www.shodor.org/interactivate/guide/Activities and tools:
http://www.shodor.org/interactivate/activities/
Language
Arts
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
7 Matrix
Accelerated 7
Matrix
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6